One of the things that you would need to do is make sure the original owner remove the phone from his account. To do this :
- Go to windowsphone.com
- Let the original owner sign-in with his Microsoft account
- Go to account settings
- Click on the "Remove this phone" for that phone

This make sure that the phone is no longer tied to the original owner account and enables you to tied it to your account instead.

The other things is would probably be basic stuff like checking the whether the IMEI code is the same as the one on the box (type *#06# on the dialer).